North Carolina State University Team Designs Quantum Signal Processing for Robust Quantum Control

Aishwarya Majumdar and colleagues at North Carolina State University, in collaboration with Northwest National Laboratory, University of Toronto, and Harvard University, have presented a new analytical framework called QSP-Control for managing qubit-oscillator dynamics. The framework addresses limitations in current quantum control techniques that often rely on inefficient optimisation methods, instead using the strong error guarantees of quantum algorithms. By applying quantum signal processing, the team mitigates unwanted nonlinear effects and designs operators for precise manipulation of Fock states, demonstrating a systematic and interpretable approach to solving key problems in quantum control. It provides a flexible set of tools for precisely controlling quantum systems, a vital step towards building practical quantum computers.

Selective Fock state control via quantum signal processing enables enhanced qubit-oscillator

Scientists at North Carolina State University, alongside collaborators at the University of Toronto and Harvard University, have developed a new analytical framework, QSP-Control, for manipulating qubit-oscillator systems. It surpasses previous methods by enabling precise control over Fock states, a key step towards advanced quantum technologies. Existing techniques lacked the ability to selectively target individual Fock states without affecting others, hindering progress in the field. Fock states, representing the number of photons in a harmonic oscillator, are crucial for encoding and processing quantum information, and their precise control is paramount for maintaining coherence and fidelity in quantum operations. The inability to address these states individually has historically necessitated complex calibration procedures and limited the scalability of quantum circuits.

The team’s approach uses quantum signal processing, a technique for designing quantum algorithms, to minimise unwanted interactions and achieve this level of precision. Quantum signal processing allows for the implementation of arbitrary functions of a Hermitian operator using a sequence of controlled operations. Drawing parallels between the Jaynes-Cummings interaction and quantum signal processing has created a systematic and interpretable design for quantum control, moving beyond the limitations of trial-and-error optimisation. The Jaynes-Cummings model describes the interaction between a single mode of the electromagnetic field and a two-level atom (or qubit), and its connection to quantum signal processing provides a rigorous mathematical foundation for pulse design. The effectiveness of QSP-Control was demonstrated by successfully approximating cosine values essential for linear phase calculations, a fundamental requirement for many quantum algorithms and control sequences. These cosine approximations are critical for implementing phase gates and other essential quantum operations with high accuracy.

Results utilising polynomial degrees of 50, 100, and 200 revealed a reduction in ripples within the polynomial approximations near zero and target values. These ripples represent errors in the control pulses, and their reduction is directly correlated with improved fidelity of the quantum operations. A packing condition for rectangular bands of width ‘w’, separated by transition regions of width ‘δ’, was also established, ensuring the Fock levels remain within a defined interval; this condition dictates that Ncutoffw + (Ncutoff −1)δ ≤Ncutoff, where Ncutoff represents the upper limit of Fock levels. This packing condition is essential for preventing unwanted transitions between Fock states during the control process, thereby maintaining the integrity of the quantum information. The Jaynes-Cummings interaction, a fundamental process in cavity quantum electrodynamics, can be decomposed into operations acting on two-dimensional subspaces, mirroring an interleaved term within a quantum signal processing sequence. This decomposition allows for the efficient implementation of complex control pulses using a relatively small number of quantum gates.

Analytical pulse design enhances understanding of qubit-oscillator dynamics

Stable quantum computation relies on our ability to control qubits and oscillators with ever-increasing precision, demanding a shift away from the often unpredictable nature of trial-and-error methods. While the current form of this framework focuses specifically on qubit-oscillator systems, this limitation is reasonable given the breadth of quantum computing approaches. However, the team’s analytical method offers a vital advantage over existing trial-and-error techniques; it provides a systematic way to design control pulses, improving understanding of how quantum systems respond. Traditional optimisation methods often yield solutions that are difficult to interpret, making it challenging to identify the underlying principles governing the system’s behaviour. This lack of interpretability hinders the development of more robust and efficient control strategies.

This detailed insight is valuable even with current limitations, potentially accelerating progress across diverse quantum platforms by informing future, more broadly applicable control strategies. The approach addresses unwanted nonlinear effects stemming from cross-Kerr interactions, disturbances that complicate control. Cross-Kerr interactions arise from the coupling between multiple qubits and can introduce errors in quantum computations. By mitigating these interactions, QSP-Control enhances the stability and accuracy of quantum operations. Designing operators to precisely manipulate Fock states, representing specific energy levels within the system, demonstrates a systematic approach to quantum control problems. The ability to selectively address and control these energy levels is crucial for implementing complex quantum algorithms and performing high-fidelity quantum simulations. This advance offers an interpretable design framework, potentially accelerating the development of more durable quantum technologies and opening questions regarding its application to diverse quantum platforms. Further research could explore the extension of QSP-Control to other quantum systems, such as trapped ions or superconducting circuits, and investigate its potential for optimising more complex quantum algorithms. The framework’s analytical nature allows for a deeper understanding of the control landscape, potentially leading to the discovery of novel control strategies and improved quantum device performance. The rigorous error guarantees inherent in quantum algorithms provide a solid foundation for building reliable and scalable quantum computers.

The researchers demonstrated a new analytical framework, QSP-Control, for managing qubit-oscillator dynamics. This method offers a greater understanding of how quantum systems respond to control signals, unlike traditional optimisation techniques which often lack interpretability. By mitigating unwanted nonlinear effects from cross-Kerr interactions and enabling precise manipulation of Fock states, the framework enhances the stability and accuracy of quantum operations. The authors suggest extending this approach to other quantum systems, potentially informing the development of more robust quantum technologies.